ANALYSIS AND FITTING OF AN SIR MODEL WITH HOST RESPONSE TO INFECTION LOAD FOR A PLANT-DISEASE

We reformulate a model for botanical epidemics into an SIR form for su sceptible (S), infected (I) and removed (R) plant organs, in order to examine the effects of different models for the effect of host respons es to the load of infection on the production of susceptible tissue. T he new formulation also allows for a decline in host susceptibility wi th age. The model is analysed and tested for the stem canker disease o f potatoes, caused by the soil-borne fungus, Rhizoctonia solani. Using a combination of model fitting to field data and analysis of model be haviour, we show that a function for host response to the amount (load ) of parasite infection is critical in the description of the temporal dynamics of susceptible and infected stems in epidemics of R. solani. Several different types of host response to infection are compared in cluding two that allow for stimulation of the plant to produce more su sceptible tissue at low levels of disease and inhibition at higher lev els. We show that when the force of infection decays with time, due to increasing resistance of the host, the equilibrium density of suscept ible stems depends on the parameters and initial conditions. The model s differ in sensitivity to small changes in disease transmission with some showing marked qualitative changes leading to a flush of suscepti ble stems at low levels of disease transmission. We conclude that ther e is no evidence to reject an SIR model with a simpler linear term for the effect of infection load on the production of healthy tissue, eve n though biological considerations suggest greater complexity in the r elationship between disease and growth. We show that reduction in init ial inoculum density, and hence in the force of infection, is effectiv e in controlling disease when the simple model applies.